Three-dimensional photoelasticity analysis of Nitinol Patellar Concentrator for treating patellar fractures

Objective: To analyze the biomechanical elements of Nitinol Patellar Concentrator (NT-PC) in heating commi nuted patellar fractures. Methods: The epoxy resin three dimensional photoelasticity pobal model was loaded with Nitinol Patellar Connector and frozen. After dividing layer, photographing and tracing, iterative method was used to calculate the stress value of every tuteed node. Rasults: Stress values of 1 262 nodes scattered in 12 layers were obtained The stress distribution indicated that an overall stress field was yield when the NT-PC fixated the patellar model, and there existed fixative stress in the facies articularis and distal pole of the patellar model. Conclusion: The NT-PC has evident therapeutic effect for the comminuted patellar fractures. The existing stress is helpful in maintaining anatomical reduction and enhancing fracture healing.

Propagation Properties of Backward Lamb Waves in Plate Investigated by Dynamic Photoelastic Technique

The dynamic photoelastic technique is employed to visualize and quantify the propagation properties of backward Lamb waves in a plate. Higher energy leaikage of second-order symmetric backward wave mode S_(2 b) in contrast to third-order anti-symmetric backward mode A3 b is shown by the dispersion curve of a plate immersed in water,and then verified by experiments. To avoid the considerable high leakage, the plate is placed in air, both group and phase velocities of modes S_(2 b) and A3 b in the glass plate are experimentally measured. In comparison with the theoretical values, less than 5% errors are found in experiments.

THE VARIATIONAL PRINCIPLES OF COUPLED SYSTEMS IN PHOTOELASTICITY

ＴＨＥＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＯＦＣＯＵＰＬＥＤＳＹＳＴＥＭＳＩＮＰＨＯＴＯＥＬＡＳＴＩＣＩＴＹＦｕＢａｏ－ｌｉａｎ（付宝连）（ＹａｎｓｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｑｉｎｈｕａｎｇｄａｏ）（ＲｅｃｅｉｖｅｄＮｏｖ．８，１９８９，Ｃｏ...

High-precision stress determination in photoelasticity

Stress separation is usually achieved by solving differential equations of equilibrium after parameter determination from isochromatics and isoclinics.The numerical error resulting from the stress determination is a main concern as it is always a function of parameters in discretization.To improve the accuracy of stress calculation,a novel meshless barycentric rational interpolation collocation method(BRICM)is proposed.The derivatives of the shear stress on the calculation path are determined by using the differential matrix which converts the differential form of the equations of equilibrium into a series of algebraic equations.The advantage of the proposed method is that the auxiliary lines,grids,and error accumulation which are commonly used in traditional shear difference methods(SDMs)are not required.Simulation and experimental results indicate that the proposed meshless method is able to provide high computational accuracy in the full-field stress determination.

Analysis of the Stress Distribution Pattern of Anatomic and Non-Anatomic Tooth Forms on Maxillary and Mandibular Edentulous Ridges—A Photoelastic Study

Aim: To compare the type of stress distribution pattern occurring with anatomic and non-anatomic tooth forms beneath a complete denture in both maxillary and mandibular arch. Methodology: A photoelastic model of the edentulous maxillary and mandibular ridge was prepared meticulously to simulate the human mandible and maxilla. Two sets of acrylic teeth with anatomic and non-anatomic occlusal forms were used to fabricate upper and lower dentures. A vertical static load of 100 N was applied through the mandibular model to the maxillary model. After load application on the dentures the photoelastic model as well as the upper and lower complete dentures were sectioned in the midline. The sectioned photoelastic model was viewed through a polariscope to observe the fringe pattern indicating varying amounts of stress distribution. In this study, a two-dimensional photoelastic stress analysis technique was utilized. Results: Force per unit area was observed more in anatomic teeth than the non-anatomic counterpart. Hence anatomic tooth forms may increase the possibility of bone resorption rate over a period of time. However, in non-anatomic lower teeth, a decrease in value was observed from posterior to anterior region. Conclusion: Stress of greater magnitude was observed with cuspal teeth whereas non-anatomic (0°) showed slightly less magnitude of stress. Depending upon the clinical situation the clinician needs to choose the type of occlusal tooth forms for edentulous patients.

SEPARATION OF PRINCIPAL STRESSES IN DYNAMIC PHOTOELASTICITY

A new and effective method used to separate the transient principalstresses for dynamic photoelasticity is proposed. This is a hybrid method combiningthe optical method of dynamic caustics and the boundary element numerical method.Firstly, a modified Cranz-Schardin spark camera is used to record simultaneouslythe isochromatic fringe patterns of photoelasticity and the shadow spot patterns inthe dynamic process. By means of the isochromatic fringe patterns, the differencebetween transient principal stresses in the whole domain and the principal stressesalong the free boundary can be solved. In addition, the method of caustics is avery powerful technique for measuring the concentrative load. Then, the sum of theprincipal stresses is calculated by the boundary integral equation obtained from theLaplace integral transform of the wave equation. So, the transient principal stressescan be determined from the experimental and numerical results. As an example, thetransient principal stresses in a polycarbonate disk under an impact load are resolved.

COUPLED VARIATIONAL PRINCIPLES AND GENERALIZED COUPLED VARIATIONAL PRINCIPLES IN PHOTOELASTICITY

ＦｕＢａｏｌｉａｎ（付宝连）（ＲｅｃｅｉｖｅｄＮｏｖ．２２，１９９３；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅｎＷｅｉｚａｎｇ）ＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩＮＣＩＰＬＥＳＡＮＤＧＥＮＥＲＡＬＩＺＥＤＣＯＵＰＬＥＤＶＡＲＩＡＴＩＯＮＡＬＰＲＩ...

Determination of the full-field stress and displacement using photoelasticity and sampling moirémethod in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials.Various optical measurement techniques such as photoelasticity,moiréand digital image correlation methods have been developed to achieve this goal.However,these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement;however,these elements will disturb the light passing through the tested models using photoelasticity.In this study,by combining photoelasticity and the sampling moirémethod,we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional(3D)-printed photoelastic model with orthogonal grating.Then,the full-field stress was determined by analyzing 10 photoelastic patterns,and the displacement fields were calculated using the sampling moirémethod.The results indicate that the developed method can simultaneously determine the stress and displacement fields.

Modeling of Orientation-Dependent Photoelastic Constants in Cubic Crystal System

Euler’s rotation theorem and tensor rotation technique are applied to develop a generalized mathematical model for determining photoelastic constants in arbitrary orientation of cubic crystal system. Two times rotations are utilized in the model relating to crystallographic coordinates with Cartesian coordinates. The symmetry of photoelastic constants is found to have strong dependence with rotation angle. Using the model, one can determine photoelastic constants in any orientation by selecting appropriate rotation angle. The outcome of this study helps to characterize spatial variation of residual strain in crystalline as well as polycrystalline materials having cubic structure using the experimental technique known as scanning infrared polariscope.

Crack-Tip Stress Analysis at a Bi-Material Interface by Photoelastic, Isopachic and FEA

The paper investigates the stress state at the bi-material interface crack-tip by the Photoelastic and Isopachic methods and the Finite Element Analysis (FEA). The principal stresses at the bi-material interface crack-tip are theoretically determined using the combination photoelastic and isopachic fringes. The size and the shape of crack-tip isochro-matic and isopachic fringes, at a bi-material interface under static load, are studied. When the crack-tip, which is perpendicular to interface, is placed at the interface of the bi-material, the isochromatic and the isopachic fringes depend on the properties of the two materials. Thus, the isochromatic and the isopachic fringes are divided into two branches, which present a jump of values at the interface. The size of the two branches mainly depends on the elastic modulus and the Poisson’s ratio of the two materials. From the combination of the isochromatic and the isopachic fringes, the principal stresses σ1 and σ2 can be estimated and the contour curves around the crack-tip can be plotted. For the FEA analysis, the program ANSYS 11.0 was used. The bi-material cracked plates were made from Lexan (BCBA) and Plexiglas (PMMA).

Characterization of Electrical Tree Degradation of Epoxy Resin under Thermal and Temperature Stresses by Photoelastic Effect

Epoxy resin is widely used in the support,insulation,and packaging components of electrical equipment owing to their excellent insulation,thermal,and mechanical properties.However,epoxy-resin insulation often suffers from thermal and mechanical stresses under extreme environmental conditions and a compact design,which can induce electrical tree degradation and insulation failure in electrical equipment.In this study,the photoelastic method is employed to investigate the thermal-mechanical coupling stress dependence of the electrical treeing behavior of epoxy resin.Typical electrical tree growth morphology and stress distribution were observed using the photoelastic method.The correlation between the tree length and overall accumulated damage with an increase in mechanical stress is determined.The results show that compressive stress retards the growth of electrical trees along the electric field,while tensile stress has accelerating effects.This proves that the presence of thermal stress can induce more severe accumulated damage.

Automatic extraction method of force chain information and its application in the flow photoelastic experiment of granular matter

The force chain is the core of the multi-scale analysis of granular matter.Accurately extracting the force chain information among particles is of great significance to the study of particle mechanics and geological hazards caused by particle flow.However,in the photoelastic experiment,the precise identification of the branching points of force chains has not been effectively realized.Therefore,this study proposes an automatic extraction method of force chain key information.First,based on the Hough transform and the Euclidean distance,a particle geometric information identification model is established and geometric information such as particle circle center coordinates,radius,contact point location,and contact angle is extracted.Then,a particle contact force information identification model is established following the color gradient mean square method.The model realizes the rapid calibration and extraction of a large number of particle media contact force information.Next,combined with the force chain composition criterion and its quasilinear feature,an automatic extraction method of force chain information is established,which solves the problem of the accurate identification of the force chain branch points.Finally,in the photoelastic experiment of ore drawing from a single drawpoint,the automatic extraction method of force chain information is verified.The results show that the macroscopic distribution of force chains during ore drawing from a single drawpoint is left–right symmetrical.Strong force chains are mostly located on the two sides of the model but in small numbers and they mainly develop vertically.Additionally,the ends are mostly in a combination of Y and inverted Y shapes,while the middle is mostly quasilinear.Weak force chains are abundant and mostly distributed in the middle of the model,and develop in different directions.The proposed extraction method accurately extracts the force chain network from the photoelastic experiment images and dynamically characterizes the force chains of granular matter,which has significant advantages in particle geometry information extraction,force chain branch point discrimination,force chain retrieval,and force chain distribution and its azimuthal characterization.The results provide a scientific basis for studying the macroscopic and microscopic mechanical parameters of granular matter.

Application of artificial neural networks for stress state analysis based on the photoelastic method

The present article proposes an evolutionary development of the photoelasticity method for measuring stresses based on annular photoelastic sensors application along with stress pattern recording with the aid of a digital camera and its recognition using artificial neural networks.The analysis of the modern application of the photoelasticity method for various problems within the theory of strength is presented.The principle of operation of photoelastic sensors based on the photoelasticity effect is considered.Optical patterns in an annular photoelastic sensor are presented for various values of the horizontal stress.The calculation of the stress state of the sensor for the following full-scale experiment has been performed,the estimate of the threshold conditions under which the sensor can be applied has been performed.As a result of a laboratory experiment,a dataset of 1500 isochromatic images has been assembled.A subspecies of a neural network,namely a convolutional neural network,has been applied as a machine learning algorithm.Different combination of models and optimizers have been employed.The application of downhole sensors for continuous monitoring of alterations in the rock mass stress state and the integration of this data into a digital field model based on Internet of Things technologies has been proposed.

UTILIZING PHASE RETARD INTEGRATION METHOD OF FLOW BIREFRINGENCE TO ANALYSE THE FLOW WITH SYMMETRIC PLANE

The formulas which are suitable to birefringent medium with symmetric plane are derived bymeans of phase retard integration.We have adopted this concept to the axisymmetric problems and deducedsome useful formulas for these cases.As a practical application,the strain rate analysis of flow in adiverging or a converging vessel is illustrated at the end of this paper.

EXPERIMENTAL STUDY ON CRACK CURVING PROPAGATION IN BENDING BEAMS UNDER IMPULSIVE LOAD

Dynamic fracture behaviour of crack curving in bent beams has beeninvestigated.In order to understand the propagation mechanism of such cracks underimpact,an experimental method is used that combines dynamic photoelasticity withdynamic caustics to study the interaction of the flexural waves and the crack.Fromthe state change of the transient stresses in polymer specimen,the curving fracturein the impulsively loaded beams is analyzed.The dynamic responses of crack tips areevaluated by the stress intensity factors for the cracks running in varying curvaturepaths under bending stress wave.

The Mathematical Foundations of Elasticity and Electromagnetism Revisited

The first purpose of this striking but difficult paper is to revisit the mathematical foundations of Elasticity (EL) and Electromagnetism (EM) by comparing the structure of these two theories and examining with details their known couplings, in particular piezoelectricity and photoelasticity. Despite the strange Helmholtz and Mach-Lippmann analogies existing between them, no classical technique may provide a common setting. However, unexpected arguments discovered independently by the brothers E. and F. Cosserat in 1909 for EL and by H. Weyl in 1918 for EM are leading to construct a new differential sequence called Spencer sequence in the framework of the formal theory of Lie pseudo groups and to introduce it for the conformal group of space-time with 15 parameters. Then, all the previous explicit couplings can be deduced abstractly and one must just go to a laboratory in order to know about the coupling constants on which they are depending, like in the Hooke or Minkowski constitutive relations existing respectively and separately in EL or EM. We finally provide a new combined experimental and theoretical proof of the fact that any 1-form with value in the second order jets (elations) of the conformal group of space-time can be uniquely decomposed into the direct sum of the Ricci tensor and the electromagnetic field. This result questions the mathematical foundations of both General Relativity (GR) and Gauge Theory (GT). In particular, the Einstein operator (6 terms) must be thus replaced by the adjoint of the Ricci operator (4 terms only) in the study of gravitational waves.

Stress Concentrations for Slotted Plates in Bi-Axial Stress

The photo-elastic method has been employed to determine stress concentration factor (SCF) for square plates containing holes and inclined slots when the plate edges are subjected to in-plane tension combined with compression. Analyses given of the isochromatic fringe pattern surrounding the hole provides the SCF conveniently. The model material is calibrated from the known solution to the stress raiser arising from a small circular hole in a plate placed under biaxial tension-compression. These results also compare well with a plane stress FE analysis. Consequently, photo-elasticity has enabled SCF’s to be determined experimentally for a biaxial stress ratio, nominally equal to –4, in plates containing a long, thin slot arranged to be in alignment with each stress axis. The two, principal stresses lying along axes of symmetry in the region surrounding the notch are separated within each isochromatic fringe by the Kuske method [1]. FE provides a comparable full-field view in which contours of maximum shear stress may be identified with the isochromatic fringe pattern directly. The principal stress distributions referred to the plate axes show their maximum concentrations at the notch boundary. Here up to a fourfold magnification occurs in the greater of the two nominal stresses under loads applied to the plate edges. Thus, it is of importance to establish the manner in which the tangential stress is distributed around the slot boundary. Conveniently, it is shown how this distribution is also revealed from an isochro-matic fringe pattern, within which lie the points of maximum tension and maximum compression.

New Methods of Determining the Mixed Mode Stress Intensity Factors for V-Shaped Notch

In this paper, on the basis of the stress field given by D.H.Chen, three new photoelastic methods are developed for determining the stress intensity factors K1 and K2 of V-shaped notch. Some photoelastic experiments are performed on a skew -symmetric 45° notch. Measurements of the coordinates components of r,θand fringe order N are made for progressively smaller fringes and used in the proposed methods to solve K1 and K2.Plots of apparent K vs. r/l are made and extrapolated to the notch tip to yield the true values of K1 and K2.The results obtained by the three methods are very close to each other. When the notch problem is simplified as a crack problem, the corresponding equation is identical to the one proposed by D.G. Smith, which shows that the proposed methods are applicable for both notch and crack problems.

A SIMPLE METHOD OF DETERMINING STRESS INTENSITY FACTOR K_I FROM ISOCHROMATIC FRINGE LOOPS

Ｏｗｉｎｇｔｏｔｈｅｉｍｐｏｒｔａｎｃｅｏｆｓｔｒｅｓｓｉｎｔｅｎｓｉｔｙｆａ－ｔｏｒｉｎｌｉｎｅａｒ－ｅｌａｓｔｉｃｆｒａｃｔｕｒｅｍｅｃｈａｎｉｃｓ，ｃｏｎｓｉｄｅｒ－ａｂｌｅｒｅｓｅａｒｃｈｉｓｃｏｎｄｕｃｔｅｄｉｎｂｏｔｈｔｈｅｏｒｙａｎｄｅ...

A MIXED METHOD OF SOLUTION FOR CONTACT STRESSES ON ROLLER

A mixed method of solution for contact stresses on rollers was suggested by the combina-tion of similitude principle.photoelastic method,Hertz’s contact theory and numericalcalculation.Thus,not only the distribution regularity of axial contact pressure on rollerof limited length,but also the three-dimensional solution of stresses in the contact po-sitions may be obtained.An actual example is presented in the paper.It shows thatthe practical damaged phenomenon in real roller is in agreement with the result of